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revision 1.2 by cnh, Mon Oct 22 11:55:48 2001 UTC revision 1.16 by jmc, Tue Jan 15 20:04:06 2008 UTC
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1  % $Header$  % $Header$
2  % $Name$  % $Name$
3    
4  \section{Example: 4$^\circ$ Global Climatological Ocean Simulation}  \section[Global Ocean MITgcm Exmaple]{Global Ocean Simulation at $4^\circ$ Resolution}
5  \label{sec:eg-global}  \label{www:tutorials}
6    \label{sect:eg-global}
7    \begin{rawhtml}
8    <!-- CMIREDIR:eg-global: -->
9    \end{rawhtml}
10    \begin{center}
11    (in directory: {\it verification/tutorial\_global\_oce\_latlon/})
12    \end{center}
13    
14  \bodytext{bgcolor="#FFFFFFFF"}  \bodytext{bgcolor="#FFFFFFFF"}
15    
16  %\begin{center}  %\begin{center}
17  %{\Large \bf Using MITgcm to Simulate Global Climatalogical Ocean Circulation  %{\Large \bf Using MITgcm to Simulate Global Climatological Ocean Circulation
18  %At Four Degree Resolution with Asynchronous Time Stepping}  %At Four Degree Resolution with Asynchronous Time Stepping}
19  %  %
20  %\vspace*{4mm}  %\vspace*{4mm}
# Line 16  Line 23 
23  %{\large May 2001}  %{\large May 2001}
24  %\end{center}  %\end{center}
25    
 \subsection{Introduction}  
   
 This document describes the third example MITgcm experiment. The first  
 two examples illustrated how to configure the code for hydrostatic idealised  
 geophysical fluids simulations. This example iilustrates the use of  
 the MITgcm for large scale ocean circulation simulation.  
   
 \subsection{Overview}  
26    
27  This example experiment demonstrates using the MITgcm to simulate  This example experiment demonstrates using the MITgcm to simulate
28  the planetary ocean circulation. The simulation is configured  the planetary ocean circulation. The simulation is configured
29  with realistic geography and bathymetry on a  with realistic geography and bathymetry on a
30  $4^{\circ} \times 4^{\circ}$ spherical polar grid.  $4^{\circ} \times 4^{\circ}$ spherical polar grid.
31    The files for this experiment are in the verification directory
32    under tutorial\_global\_oce\_latlon.
33  Twenty levels are used in the vertical, ranging in thickness  Twenty levels are used in the vertical, ranging in thickness
34  from $50\,{\rm m}$ at the surface to $815\,{\rm m}$ at depth,  from $50\,{\rm m}$ at the surface to $815\,{\rm m}$ at depth,
35  giving a maximum model depth of $6\,{\rm km}$.  giving a maximum model depth of $6\,{\rm km}$.
# Line 36  At this resolution, the configuration Line 37  At this resolution, the configuration
37  can be integrated forward for thousands of years on a single  can be integrated forward for thousands of years on a single
38  processor desktop computer.  processor desktop computer.
39  \\  \\
40    \subsection{Overview}
41    \label{www:tutorials}
42    
43  The model is forced with climatalogical wind stress data and surface  The model is forced with climatological wind stress data and surface
44  flux data from DaSilva \cite{DaSilva94}. Climatalogical data  flux data from DaSilva \cite{DaSilva94}. Climatological data
45  from Levitus \cite{Levitus94} is used to initialise the model hydrography.  from Levitus \cite{Levitus94} is used to initialize the model hydrography.
46  Levitus seasonal clmatology data is also used throughout the calculation  Levitus seasonal climatology data is also used throughout the calculation
47  to provide additional air-sea fluxes.  to provide additional air-sea fluxes.
48  These fluxes are combined with the DaSilva climatalogical estimates of  These fluxes are combined with the DaSilva climatological estimates of
49  surface heat flux and fresh water, resulting in a mixed boundary  surface heat flux and fresh water, resulting in a mixed boundary
50  condition of the style decribed in Haney \cite{Haney}.  condition of the style described in Haney \cite{Haney}.
51  Altogether, this yields the following forcing applied  Altogether, this yields the following forcing applied
52  in the model surface layer.  in the model surface layer.
53    
54  \begin{eqnarray}  \begin{eqnarray}
55  \label{EQ:global_forcing}  \label{EQ:eg-global-global_forcing}
56  \label{EQ:global_forcing_fu}  \label{EQ:eg-global-global_forcing_fu}
57  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}
58  \\  \\
59  \label{EQ:global_forcing_fv}  \label{EQ:eg-global-global_forcing_fv}
60  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}
61  \\  \\
62  \label{EQ:global_forcing_ft}  \label{EQ:eg-global-global_forcing_ft}
63  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )
64   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}
65  \\  \\
66  \label{EQ:global_forcing_fs}  \label{EQ:eg-global-global_forcing_fs}
67  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )
68   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})
69  \end{eqnarray}  \end{eqnarray}
# Line 87  have units of ${\rm N}~{\rm m}^{-2}$. Th Line 90  have units of ${\rm N}~{\rm m}^{-2}$. Th
90  ($\theta^{\ast}$ and $Q$) have units of $^{\circ}{\rm C}$ and ${\rm W}~{\rm m}^{-2}$  ($\theta^{\ast}$ and $Q$) have units of $^{\circ}{\rm C}$ and ${\rm W}~{\rm m}^{-2}$
91  respectively. The salinity forcing fields ($S^{\ast}$ and  respectively. The salinity forcing fields ($S^{\ast}$ and
92  $\cal{E}-\cal{P}-\cal{R}$) have units of ${\rm ppt}$ and ${\rm m}~{\rm s}^{-1}$  $\cal{E}-\cal{P}-\cal{R}$) have units of ${\rm ppt}$ and ${\rm m}~{\rm s}^{-1}$
93  respectively.  respectively. The source files and procedures for ingesting this data into the
94  \\  simulation are described in the experiment configuration discussion in section
95    \ref{SEC:eg-global-clim_ocn_examp_exp_config}.
   
 Figures (\ref{FIG:sim_config_tclim}-\ref{FIG:sim_config_empmr}) show the  
 relaxation temperature ($\theta^{\ast}$) and salinity ($S^{\ast}$) fields,  
 the wind stress components ($\tau_x$ and $\tau_y$), the heat flux ($Q$)  
 and the net fresh water flux (${\cal E} - {\cal P} - {\cal R}$) used  
 in equations \ref{EQ:global_forcing_fu}-\ref{EQ:global_forcing_fs}. The figures  
 also indicate the lateral extent and coastline used in the experiment.  
 Figure ({\ref{FIG:model_bathymetry}) shows the depth contours of the model  
 domain.  
96    
97    
98  \subsection{Discrete Numerical Configuration}  \subsection{Discrete Numerical Configuration}
99    \label{www:tutorials}
100    
101    
102   The model is configured in hydrostatic form.  The domain is discretised with   The model is configured in hydrostatic form.  The domain is discretised with
# Line 109  a uniform grid spacing in latitude and l Line 104  a uniform grid spacing in latitude and l
104   $\Delta \phi=\Delta \lambda=4^{\circ}$, so   $\Delta \phi=\Delta \lambda=4^{\circ}$, so
105  that there are ninety grid cells in the zonal and forty in the  that there are ninety grid cells in the zonal and forty in the
106  meridional direction. The internal model coordinate variables  meridional direction. The internal model coordinate variables
107  $x$ and $y$ are initialised according to  $x$ and $y$ are initialized according to
108  \begin{eqnarray}  \begin{eqnarray}
109  x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\  x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\
110  y=r\lambda,~\Delta x &= &r\Delta \lambda  y=r\lambda,~\Delta y &= &r\Delta \lambda
111  \end{eqnarray}  \end{eqnarray}
112    
113  Arctic polar regions are not  Arctic polar regions are not
# Line 146  $ Line 141  $
141   \Delta z_{18}=725\,{\rm m},\,   \Delta z_{18}=725\,{\rm m},\,
142   \Delta z_{19}=775\,{\rm m},\,   \Delta z_{19}=775\,{\rm m},\,
143   \Delta z_{20}=815\,{\rm m}   \Delta z_{20}=815\,{\rm m}
144  $ (here the numeric subscript indicates the model level index number, ${\tt k}$).  $ (here the numeric subscript indicates the model level index number, ${\tt k}$) to
145    give a total depth, $H$, of $-5450{\rm m}$.
146  The implicit free surface form of the pressure equation described in Marshall et. al  The implicit free surface form of the pressure equation described in Marshall et. al
147  \cite{Marshall97a} is employed. A laplacian operator, $\nabla^2$, provides viscous  \cite{marshall:97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous
148  dissipation. Thermal and haline diffusion is also represented by a laplacian operator.  dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.
149    
150  Wind-stress forcing is added to the momentum equations for both  Wind-stress forcing is added to the momentum equations in (\ref{EQ:eg-global-model_equations})
151  the zonal flow, $u$ and the merdional flow $v$, according to equations  for both the zonal flow, $u$ and the meridional flow $v$, according to equations
152  (\ref{EQ:global_forcing_fu}) and (\ref{EQ:global_forcing_fv}).  (\ref{EQ:eg-global-global_forcing_fu}) and (\ref{EQ:eg-global-global_forcing_fv}).
153  Thermodynamic forcing inputs are added to the equations for  Thermodynamic forcing inputs are added to the equations
154    in (\ref{EQ:eg-global-model_equations}) for
155  potential temperature, $\theta$, and salinity, $S$, according to equations  potential temperature, $\theta$, and salinity, $S$, according to equations
156  (\ref{EQ:global_forcing_ft}) and (\ref{EQ:global_forcing_fs}).  (\ref{EQ:eg-global-global_forcing_ft}) and (\ref{EQ:eg-global-global_forcing_fs}).
157  This produces a set of equations solved in this configuration as follows:  This produces a set of equations solved in this configuration as follows:
158    
159  \begin{eqnarray}  \begin{eqnarray}
160  \label{EQ:model_equations}  \label{EQ:eg-global-model_equations}
161  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
162    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
163    \nabla_{h}\cdot A_{h}\nabla_{h}u -    \nabla_{h}\cdot A_{h}\nabla_{h}u -
# Line 210  g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} d Line 207  g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} d
207  $v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$  $v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$
208  are the zonal and meridional components of the  are the zonal and meridional components of the
209  flow vector, $\vec{u}$, on the sphere. As described in  flow vector, $\vec{u}$, on the sphere. As described in
210  MITgcm Numerical Solution Procedure \cite{MITgcm_Numerical_Scheme}, the time  MITgcm Numerical Solution Procedure \ref{chap:discretization}, the time
211  evolution of potential temperature, $\theta$, equation is solved prognostically.  evolution of potential temperature, $\theta$, equation is solved prognostically.
212  The total pressure, $p$, is diagnosed by summing pressure due to surface  The total pressure, $p$, is diagnosed by summing pressure due to surface
213  elevation $\eta$ and the hydrostatic pressure.  elevation $\eta$ and the hydrostatic pressure.
214  \\  \\
215    
216  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
217    \label{www:tutorials}
218    
219  The laplacian dissipation coefficient, $A_{h}$, is set to $5 \times 10^5 m s^{-1}$.  The Laplacian dissipation coefficient, $A_{h}$, is set to $5 \times 10^5 m s^{-1}$.
220  This value is chosen to yield a Munk layer width \cite{Adcroft_thesis},  This value is chosen to yield a Munk layer width \cite{adcroft:95},
221  \begin{eqnarray}  \begin{eqnarray}
222  \label{EQ:munk_layer}  \label{EQ:eg-global-munk_layer}
223  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}  && M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
224  \end{eqnarray}  \end{eqnarray}
225    
226  \noindent  of $\approx 600$km. This is greater than the model  \noindent  of $\approx 600$km. This is greater than the model
# Line 233  boundary layer is adequately resolved. Line 231  boundary layer is adequately resolved.
231  \noindent The model is stepped forward with a  \noindent The model is stepped forward with a
232  time step $\delta t_{\theta}=30~{\rm hours}$ for thermodynamic variables and  time step $\delta t_{\theta}=30~{\rm hours}$ for thermodynamic variables and
233  $\delta t_{v}=40~{\rm minutes}$ for momentum terms. With this time step, the stability  $\delta t_{v}=40~{\rm minutes}$ for momentum terms. With this time step, the stability
234  parameter to the horizontal laplacian friction \cite{Adcroft_thesis}  parameter to the horizontal Laplacian friction \cite{adcroft:95}
235  \begin{eqnarray}  \begin{eqnarray}
236  \label{EQ:laplacian_stability}  \label{EQ:eg-global-laplacian_stability}
237  S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2}  && S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2}
238  \end{eqnarray}  \end{eqnarray}
239    
240  \noindent evaluates to 0.16 at a latitude of $\phi=80^{\circ}$, which is below the  \noindent evaluates to 0.16 at a latitude of $\phi=80^{\circ}$, which is below the
# Line 247  $\phi=80^{\circ}$ where $\Delta x=r\cos( Line 245  $\phi=80^{\circ}$ where $\Delta x=r\cos(
245  \noindent The vertical dissipation coefficient, $A_{z}$, is set to  \noindent The vertical dissipation coefficient, $A_{z}$, is set to
246  $1\times10^{-3} {\rm m}^2{\rm s}^{-1}$. The associated stability limit  $1\times10^{-3} {\rm m}^2{\rm s}^{-1}$. The associated stability limit
247  \begin{eqnarray}  \begin{eqnarray}
248  \label{EQ:laplacian_stability_z}  \label{EQ:eg-global-laplacian_stability_z}
249  S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2}  S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2}
250  \end{eqnarray}  \end{eqnarray}
251    
252  \noindent evaluates to $0.015$ for the smallest model  \noindent evaluates to $0.015$ for the smallest model
253  level spcing ($\Delta z_{1}=50{\rm m}$) which is again well below  level spacing ($\Delta z_{1}=50{\rm m}$) which is again well below
254  the upper stability limit.  the upper stability limit.
255  \\  \\
256    
# Line 262  and $3 \times 10^{-5}~{\rm m}^{2}{\rm s} Line 260  and $3 \times 10^{-5}~{\rm m}^{2}{\rm s}
260  related to $K_{h}$ will be at $\phi=80^{\circ}$ where $\Delta x \approx 77 {\rm km}$.  related to $K_{h}$ will be at $\phi=80^{\circ}$ where $\Delta x \approx 77 {\rm km}$.
261  Here the stability parameter  Here the stability parameter
262  \begin{eqnarray}  \begin{eqnarray}
263  \label{EQ:laplacian_stability_xtheta}  \label{EQ:eg-global-laplacian_stability_xtheta}
264  S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2}  S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2}
265  \end{eqnarray}  \end{eqnarray}
266  evaluates to $0.07$, well below the stabilit limit of $S_{l} \approx 0.5$. The  evaluates to $0.07$, well below the stability limit of $S_{l} \approx 0.5$. The
267  stability parameter related to $K_{z}$  stability parameter related to $K_{z}$
268  \begin{eqnarray}  \begin{eqnarray}
269  \label{EQ:laplacian_stability_ztheta}  \label{EQ:eg-global-laplacian_stability_ztheta}
270  S_{l} = \frac{4 K_{z} \delta t_{\theta}}{{\Delta z}^2}  S_{l} = \frac{4 K_{z} \delta t_{\theta}}{{\Delta z}^2}
271  \end{eqnarray}  \end{eqnarray}
272  evaluates to $0.005$ for $\min(\Delta z)=50{\rm m}$, well below the stability limit  evaluates to $0.005$ for $\min(\Delta z)=50{\rm m}$, well below the stability limit
# Line 276  of $S_{l} \approx 0.5$. Line 274  of $S_{l} \approx 0.5$.
274  \\  \\
275    
276  \noindent The numerical stability for inertial oscillations  \noindent The numerical stability for inertial oscillations
277  \cite{Adcroft_thesis}  \cite{adcroft:95}
278    
279  \begin{eqnarray}  \begin{eqnarray}
280  \label{EQ:inertial_stability}  \label{EQ:eg-global-inertial_stability}
281  S_{i} = f^{2} {\delta t_v}^2  S_{i} = f^{2} {\delta t_v}^2
282  \end{eqnarray}  \end{eqnarray}
283    
# Line 287  S_{i} = f^{2} {\delta t_v}^2 Line 285  S_{i} = f^{2} {\delta t_v}^2
285  the $S_{i} < 1$ upper limit for stability.  the $S_{i} < 1$ upper limit for stability.
286  \\  \\
287    
288  \noindent The advective CFL \cite{Adcroft_thesis} for a extreme maximum  \noindent The advective CFL \cite{adcroft:95} for a extreme maximum
289  horizontal flow  horizontal flow
290  speed of $ | \vec{u} | = 2 ms^{-1}$  speed of $ | \vec{u} | = 2 ms^{-1}$
291    
292  \begin{eqnarray}  \begin{eqnarray}
293  \label{EQ:cfl_stability}  \label{EQ:eg-global-cfl_stability}
294  S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x}  S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x}
295  \end{eqnarray}  \end{eqnarray}
296    
# Line 300  S_{a} = \frac{| \vec{u} | \delta t_{v}}{ Line 298  S_{a} = \frac{| \vec{u} | \delta t_{v}}{
298  limit of 0.5.  limit of 0.5.
299  \\  \\
300    
301  \noindent The stability parameter for internal gravity waves propogating  \noindent The stability parameter for internal gravity waves propagating
302  with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$  with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$
303  \cite{Adcroft_thesis}  \cite{adcroft:95}
304    
305  \begin{eqnarray}  \begin{eqnarray}
306  \label{EQ:cfl_stability}  \label{EQ:eg-global-gfl_stability}
307  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x}  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x}
308  \end{eqnarray}  \end{eqnarray}
309    
# Line 313  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delt Line 311  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delt
311  stability limit of 0.5.  stability limit of 0.5.
312        
313  \subsection{Experiment Configuration}  \subsection{Experiment Configuration}
314  \label{SEC:clim_ocn_examp_exp_config}  \label{www:tutorials}
315    \label{SEC:eg-global-clim_ocn_examp_exp_config}
316    
317  The model configuration for this experiment resides under the  The model configuration for this experiment resides under the
318  directory {\it verification/exp2/}.  The experiment files  directory {\it tutorial\_examples/global\_ocean\_circulation/}.  
319    The experiment files
320    
321  \begin{itemize}  \begin{itemize}
322  \item {\it input/data}  \item {\it input/data}
323  \item {\it input/data.pkg}  \item {\it input/data.pkg}
# Line 332  directory {\it verification/exp2/}.  The Line 333  directory {\it verification/exp2/}.  The
333  \item {\it code/CPP\_OPTIONS.h},  \item {\it code/CPP\_OPTIONS.h},
334  \item {\it code/SIZE.h}.  \item {\it code/SIZE.h}.
335  \end{itemize}  \end{itemize}
336  contain the code customisations and parameter settings for these  contain the code customizations and parameter settings for these
337  experiements. Below we describe the customisations  experiments. Below we describe the customizations
338  to these files associated with this experiment.  to these files associated with this experiment.
339    
340    \subsubsection{Driving Datasets}
341    \label{www:tutorials}
342    
343    Figures (\ref{FIG:sim_config_tclim}-\ref{FIG:sim_config_empmr}) show the
344    relaxation temperature ($\theta^{\ast}$) and salinity ($S^{\ast}$) fields,
345    the wind stress components ($\tau_x$ and $\tau_y$), the heat flux ($Q$)
346    and the net fresh water flux (${\cal E} - {\cal P} - {\cal R}$) used
347    in equations \ref{EQ:global_forcing_fu}-\ref{EQ:global_forcing_fs}. The figures
348    also indicate the lateral extent and coastline used in the experiment.
349    Figure ({\ref{FIG:model_bathymetry}) shows the depth contours of the model
350    domain.
351    
352    
353  \subsubsection{File {\it input/data}}  \subsubsection{File {\it input/data}}
354    \label{www:tutorials}
355    
356  This file, reproduced completely below, specifies the main parameters  This file, reproduced completely below, specifies the main parameters
357  for the experiment. The parameters that are significant for this configuration  for the experiment. The parameters that are significant for this configuration
# Line 348  are Line 363  are
363  \begin{verbatim} tRef= 16.0 , 15.2 , 14.5 , 13.9 , 13.3 ,  \end{verbatim}  \begin{verbatim} tRef= 16.0 , 15.2 , 14.5 , 13.9 , 13.3 ,  \end{verbatim}
364  $\cdots$ \\  $\cdots$ \\
365  set reference values for potential  set reference values for potential
366  temperature and salinity at each model level in units of $^{\circ}$C and  temperature and salinity at each model level in units of $^{\circ}\mathrm{C}$ and
367  ${\rm ppt}$. The entries are ordered from surface to depth.  ${\rm ppt}$. The entries are ordered from surface to depth.
368  Density is calculated from anomalies at each level evaluated  Density is calculated from anomalies at each level evaluated
369  with respect to the reference values set here.\\  with respect to the reference values set here.\\
# Line 361  with respect to the reference values set Line 376  with respect to the reference values set
376    
377  \item Line 15,  \item Line 15,
378  \begin{verbatim} viscAz=1.E-3, \end{verbatim}  \begin{verbatim} viscAz=1.E-3, \end{verbatim}
379  this line sets the vertical laplacian dissipation coefficient to  this line sets the vertical Laplacian dissipation coefficient to
380  $1 \times 10^{-3} {\rm m^{2}s^{-1}}$. Boundary conditions  $1 \times 10^{-3} {\rm m^{2}s^{-1}}$. Boundary conditions
381  for this operator are specified later. This variable is copied into  for this operator are specified later. This variable is copied into
382  model general vertical coordinate variable {\bf viscAr}.  model general vertical coordinate variable {\bf viscAr}.
# Line 376  model general vertical coordinate variab Line 391  model general vertical coordinate variab
391  \begin{verbatim}  \begin{verbatim}
392  viscAh=5.E5,  viscAh=5.E5,
393  \end{verbatim}  \end{verbatim}
394  this line sets the horizontal laplacian frictional dissipation coefficient to  this line sets the horizontal Laplacian frictional dissipation coefficient to
395  $5 \times 10^{5} {\rm m^{2}s^{-1}}$. Boundary conditions  $5 \times 10^{5} {\rm m^{2}s^{-1}}$. Boundary conditions
396  for this operator are specified later.  for this operator are specified later.
397    
# Line 385  for this operator are specified later. Line 400  for this operator are specified later.
400  no_slip_sides=.FALSE.  no_slip_sides=.FALSE.
401  \end{verbatim}  \end{verbatim}
402  this line selects a free-slip lateral boundary condition for  this line selects a free-slip lateral boundary condition for
403  the horizontal laplacian friction operator  the horizontal Laplacian friction operator
404  e.g. $\frac{\partial u}{\partial y}$=0 along boundaries in $y$ and  e.g. $\frac{\partial u}{\partial y}$=0 along boundaries in $y$ and
405  $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.  $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.
406    
# Line 394  $\frac{\partial v}{\partial x}$=0 along Line 409  $\frac{\partial v}{\partial x}$=0 along
409  no_slip_bottom=.TRUE.  no_slip_bottom=.TRUE.
410  \end{verbatim}  \end{verbatim}
411  this line selects a no-slip boundary condition for bottom  this line selects a no-slip boundary condition for bottom
412  boundary condition in the vertical laplacian friction operator  boundary condition in the vertical Laplacian friction operator
413  e.g. $u=v=0$ at $z=-H$, where $H$ is the local depth of the domain.  e.g. $u=v=0$ at $z=-H$, where $H$ is the local depth of the domain.
414    
415  \item Line 19,  \item Line 19,
# Line 444  These settings do not apply for this exp Line 459  These settings do not apply for this exp
459  \begin{verbatim}  \begin{verbatim}
460  gravity=9.81,  gravity=9.81,
461  \end{verbatim}  \end{verbatim}
462  Sets the gravitational acceleration coeeficient to $9.81{\rm m}{\rm s}^{-1}$.\\  Sets the gravitational acceleration coefficient to $9.81{\rm m}{\rm s}^{-1}$.\\
463  \fbox{  \fbox{
464  \begin{minipage}{5.0in}  \begin{minipage}{5.0in}
465  {\it S/R CALC\_PHI\_HYD}~({\it calc\_phi\_hyd.F})\\  {\it S/R CALC\_PHI\_HYD}~({\it calc\_phi\_hyd.F})\\
# Line 568  See section \ref{SEC:cd_scheme}. Line 583  See section \ref{SEC:cd_scheme}.
583  \fbox{  \fbox{
584  \begin{minipage}{5.0in}  \begin{minipage}{5.0in}
585  {\it S/R INI\_PARMS}({\it ini\_parms.F})\\  {\it S/R INI\_PARMS}({\it ini\_parms.F})\\
586  {\it S/R CALC\_MOM\_RHS}({\it calc\_mom\_rhs.F})  {\it S/R MOM\_FLUXFORM}({\it mom\_fluxform.F})
587  \end{minipage}  \end{minipage}
588  }  }
589    
# Line 626  notes. Line 641  notes.
641  \end{small}  \end{small}
642    
643  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
644    \label{www:tutorials}
645    
646  This file uses standard default values and does not contain  This file uses standard default values and does not contain
647  customisations for this experiment.  customisations for this experiment.
648    
649  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
650    \label{www:tutorials}
651    
652  This file uses standard default values and does not contain  This file uses standard default values and does not contain
653  customisations for this experiment.  customisations for this experiment.
654    
655  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{File {\it input/windx.sin\_y}}
656    \label{www:tutorials}
657    
658  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
659  map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.  map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.
# Line 646  in MITgcm. The included matlab program { Line 664  in MITgcm. The included matlab program {
664  code for creating the {\it input/windx.sin\_y} file.  code for creating the {\it input/windx.sin\_y} file.
665    
666  \subsubsection{File {\it input/topog.box}}  \subsubsection{File {\it input/topog.box}}
667    \label{www:tutorials}
668    
669    
670  The {\it input/topog.box} file specifies a two-dimensional ($x,y$)  The {\it input/topog.box} file specifies a two-dimensional ($x,y$)
# Line 657  The included matlab program {\it input/g Line 676  The included matlab program {\it input/g
676  code for creating the {\it input/topog.box} file.  code for creating the {\it input/topog.box} file.
677    
678  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
679    \label{www:tutorials}
680    
681  Two lines are customized in this file for the current experiment  Two lines are customized in this file for the current experiment
682    
# Line 683  the vertical domain extent in grid point Line 703  the vertical domain extent in grid point
703  \end{small}  \end{small}
704    
705  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
706    \label{www:tutorials}
707    
708  This file uses standard default values and does not contain  This file uses standard default values and does not contain
709  customisations for this experiment.  customisations for this experiment.
710    
711    
712  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
713    \label{www:tutorials}
714    
715  This file uses standard default values and does not contain  This file uses standard default values and does not contain
716  customisations for this experiment.  customisations for this experiment.
717    
718  \subsubsection{Other Files }  \subsubsection{Other Files }
719    \label{www:tutorials}
720    
721  Other files relevant to this experiment are  Other files relevant to this experiment are
722  \begin{itemize}  \begin{itemize}
# Line 704  coriolis variables {\bf fCorU}. Line 727  coriolis variables {\bf fCorU}.
727  \item {\it input/windx.sin\_y},  \item {\it input/windx.sin\_y},
728  \end{itemize}  \end{itemize}
729  contain the code customisations and parameter settings for this  contain the code customisations and parameter settings for this
730  experiements. Below we describe the customisations  experiments. Below we describe the customisations
731  to these files associated with this experiment.  to these files associated with this experiment.
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